Radius of the path of an accelerating object in uniform Circular motion

In summary, the car is traveling in a circle with a velocity of 24 m/s West and a total acceleration of 9 m/s^2 at 53 degrees North of West. To find the radius, two equations for the radial acceleration can be used. These equations are F=ma and a= v^2/r. The radius can then be solved for by setting these equations equal to each other and solving for r. The final answer should be in units of km.
  • #1
Runaway
48
0

Homework Statement


A 2 kg car travels in a flat circle. At
a certain instant the velocity of the car is
24 m/s West and the total acceleration of the
car is 9 m/s
2
at 53 degrees
North of West.

What is its radius?
Answer in units of km.


Homework Equations


F=ma
w=(2pi)/T
a= w^2 r
v=wr


The Attempt at a Solution


I have no Idea where to start. But, I do know that it is accelerating because its velocity is not at a right angle to its total acceleration.
 
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  • #2
Hi Runaway! :smile:

(have a pi: π and an omega: ω and try using the X2 icon just above the Reply box :wink:)
Runaway said:
… I do know that it is accelerating because its velocity is not at a right angle to its total acceleration.

if it's moving in a circle with speed v, its components of acceleration are mv2/r radially inward, and dv/dt tangentially forward :wink:
 
  • #3
I don't follow, what equation am I supposed to take the derivative of, and when I do, won't I end up with a equation in terms of t, which isn't stated?
I'm in an algebra and trig. based physics class, so we haven't really used calculus, but I am in a calculus class right now, and we are learning how to take implicit derivatives. So I think I can handle doing the derivative, if there isn't another way to solve the problem.
 
  • #4
Hi Runaway! :wink:

You don't have to differentiate or integrate anything, the question doesn't ask you for v, it only asks for the radius.

You know the total acceleration is at 37° to the radius, so call the radius r and find two different equations for the radial (centripetal) acceleration. :smile:
 
  • #5
Thanks for your help Tim, I only read your post at a glance and saw dv/dt, which made me think that I had to use that to find the answer, but now I figured it out.
 

What is the radius of the path of an accelerating object in uniform circular motion?

The radius of the path of an accelerating object in uniform circular motion is the distance from the center of the circle to the edge of the circle. It is constant and does not change as the object moves.

How is the radius of the path of an accelerating object in uniform circular motion related to its speed?

The radius of the path of an accelerating object in uniform circular motion is inversely proportional to its speed. This means that as the speed of the object increases, the radius decreases and vice versa.

Can the radius of the path of an accelerating object in uniform circular motion be negative?

No, the radius of the path of an accelerating object in uniform circular motion cannot be negative. It is always a positive value, representing the distance from the center of the circle to the edge.

What happens to the radius of the path of an accelerating object in uniform circular motion if the force acting on it changes?

If the force acting on the object changes, the radius of the path will also change. This is because the force affects the speed of the object, which in turn affects the radius. A stronger force will result in a smaller radius, while a weaker force will result in a larger radius.

How does changing the mass of an accelerating object affect its radius of the path in uniform circular motion?

Changing the mass of an accelerating object in uniform circular motion does not directly affect its radius. However, a larger mass will require a stronger force to maintain the same speed, which will in turn result in a smaller radius. Similarly, a smaller mass will require a weaker force and result in a larger radius.

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